In the fast-moving world of information and communications technologies, one significant issue in metropolitan cities is water scarcity and the need for an intelligent water distribution system for sustainable water management. An IoT-based monitoring system can improve water distribution system management and mitigate challenges in the distribution network networks such as leakage, breakage, theft, overflow, dry running of pumps and so on. However, the increase in the number of communication and sensing devices within smart cities has evoked challenges to existing communication networks due to the increase in delay and energy consumption within the network. The work presents different strategies for efficient delay and energy offloading in IoT-integrated water distribution systems in smart cities. Different IoT-enabled communication network topology diagrams are proposed, considering the different water network design parameters, land cover patterns and wireless channels for communication. From these topologies and by considering all the relevant communication parameters, the optimum communication network architecture to continuously monitor a water distribution network in a metropolitan city in India is identified. As a case study, an IoT design and analysis model is studied for a secondary metropolitan city in India. The selected study area is in Kochi, India. Based on the site-specific model and land use and land cover pattern, delay and energy modeling of the IoT-based water distribution system is discussed. Algorithms for node categorisation and edge-to-fog allocation are discussed, and numerical analyses of delay and energy models are included. An approximation of the delay and energy of the network is calculated using these models. On the basis of these study results, and state transition diagrams, the optimum placement of fog nodes linked with edge nodes and a cloud server could be carried out. Also, by considering different scenarios, up to a 40% improvement in energy efficiency can be achieved by incorporating a greater number of states in the state transition diagram. These strategies could be utilized in implementing delay and energy-efficient IoT-enabled communication networks for site-specific applications.